Geodesic
Interior GE-Filters of GE-Algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 1, pp. 217-235

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The notions of an interior GE-filter, a weak interior GE-filter and a belligerent interior GE-filter are introduced, and their relations and properties are investigated. Example of a GE-filter which is neither an interior GE-filter nor a weak interior GE-filter is provided. Relations between a weak interior GE-filter and an interior GE-filter are discussed, and conditions under which every weak interior GE-filter is an interior GE-filter are investigated. Relations between a belligerent interior GE-filter and an interior GE-filter are displayed, and conditions for an interior GE-filter to be a belligerent interior GE-filter are considered. Given a subset and an element, an interior GE-filter is established, and conditions for a subset to be a belligerent interior GE-filter are discussed. The extensibility of the beligerant interior GE-filter is debated. Relationships between weak interior GE-filter and belligerent interior GE-filter of type 1, type 2 and type 3 are founded.
Keywords: (transitive, left exchangeable) GE-algebra, GE-filter, belligerent GE-filter, (weak) interior GE-filter, belligerent interior GE-filter (of type 1, type 2 and type 3) 
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Song, Seok-Zun; Bandaru, Ravikumar; Romano, Daniel A.; Jun, Young Bae. Interior GE-Filters of GE-Algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 1, pp. 217-235. http://geodesic.mathdoc.fr/item/DMGAA_2022_42_1_a10/